#### Volume 18, issue 5 (2018)

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Modulo $2$ counting of Klein-bottle leaves in smooth taut foliations

### Boyu Zhang

Algebraic & Geometric Topology 18 (2018) 2701–2727
##### Abstract

We prove a modulo $2$ invariance for the number of Klein-bottle leaves in taut foliations. Given two smooth cooriented taut foliations, assume that every Klein-bottle leaf has nontrivial linear holonomy, and assume that the two foliations can be smoothly deformed to each other through taut foliations. We prove that the numbers of Klein-bottle leaves in these two foliations must have the same parity.

##### Keywords
taut foliations, $J$–holomorphic curves
##### Mathematical Subject Classification 2010
Primary: 57M50, 57R30, 57R57
##### Publication
Received: 14 March 2017
Revised: 23 March 2018
Accepted: 24 May 2018
Published: 22 August 2018
##### Authors
 Boyu Zhang Department of Mathematics Harvard University Cambridge, MA United States